PartialMathematician

\(f(x) = x^2-72\). y = 0 when x^2 = 72. Square rooting both sides, we find that \(x = \pm\sqrt{72}\) or \(\boxed{x = \pm 6\sqrt{2}}\).

Hope this helps,

- PM 

Georgian Language

 ათასწლეულის გამოწვევის ფონდი - საქართველო

3) Multiply the following polynomial: \((x-7)(3x^2+8)\). We do the same thing we do with a normal polynomial, we use FOIL (multiply each term). If we multiply \(x\) with \((3x^2+8)\), we get \(3x^3 + 8x\). Similarly, if we multiply \(-7\) with \((3x^2+8)\), we get \(-21x^2-56\). If we add our results, we get \(3x^3 + 8x - 21x^2 - 56 = \boxed{3x^3 - 21x^2 + 8x -56}\). 

Hope this helps,

- PM

1) From the diagram, we know the following: Angle B = Angle M = 42, Angle C = Angle N = 90, and Side BC = 4 is half of Side NM  = 8. 

Since all triangles have an interior measure of 180 degrees, if two triangles have the same measures for two angles, then the third angles must have the same measure, meaning they are similar. We also know that Triangle LMN is 2: 1 ration in side length compared to Triangle ABC. Therefore the area of Triangle LMN is 4 times larger than the area of ABC. (This is not needed in the problem though)

The answer is A, similar by AA. 

2) 2/3 divided by 14 is basically\(\dfrac{\dfrac{2}{3}}{14}\). If we multiply the numerator and denominator by \(\dfrac{\dfrac{1}{14}}{\dfrac{1}{14}}\), we have \(\dfrac{2}{3} \cdot \dfrac{1}{14} = \dfrac{1}{21}\). 

1) Simplify \(4\dfrac{3}{4}\)   to  \(\dfrac{19}{4}\), and we have our equation  \(\dfrac{5}{8}y = \dfrac{19}{4}\). By multiplying both sides by  \(\dfrac{8}{5}\), we have \(y = \dfrac{38}{5}\). 

Simplify \(-5\dfrac{3}{4}\) to \(-\dfrac{23}{4}\) and \(-3\dfrac{1}{2}\) to \(-\dfrac{7}{2}\), and we have our equation \(-\dfrac{23}{4} + x = -\dfrac{7}{2}\).  By adding \(\dfrac{23}{4}\) to both sides, we have \(x = \dfrac{9}{4}\) or \(x = 2\dfrac{1}{4}\). (\(-\dfrac{7}{2}\) --> \(-\dfrac{14}{4}\), \(\dfrac{-14 + 23}{4} = \dfrac{9}{4}\))

Hope this helps, 

- PM

Personally, I do not find you crazy for liking apples, but I do find your word "r1ght" crazy. 

Please try to limit your posts to math-related posts. Non-math posts can be tagged as "off-topic" to give other people's questions priority. 

Thanks,

- PM